{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vi2Tl3VMnX68"
      },
      "source": [
        "##### Copyright 2020 The TensorFlow Probability Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "FW9em4rqnw0S"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fpRXcosdWjaE"
      },
      "source": [
        "# TFP Release Notes notebook (0.12.1)\n",
        "\n",
        "The intent of this notebook is to help TFP 0.12.1 \"come to life\" via some small snippets - little demos of things you can achieve with TFP.\n",
        "\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/TFP_Release_Notebook_0_12_1\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/TFP_Release_Notebook_0_12_1.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/TFP_Release_Notebook_0_12_1.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://storage.googleapis.com/tensorflow_docs/probability/tensorflow_probability/examples/jupyter_notebooks/TFP_Release_Notebook_0_12_1.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oUPWBWHIHBPM"
      },
      "outputs": [],
      "source": [
        "#@title Installs & imports { vertical-output: true }\n",
        "!pip3 install -qU tensorflow==2.4.0 tensorflow_probability==0.12.1 tensorflow-datasets inference_gym\n",
        "\n",
        "import tensorflow as tf\n",
        "import tensorflow_probability as tfp\n",
        "assert '0.12' in tfp.__version__, tfp.__version__\n",
        "assert '2.4' in tf.__version__, tf.__version__\n",
        "\n",
        "physical_devices = tf.config.list_physical_devices('CPU')\n",
        "tf.config.set_logical_device_configuration(\n",
        "    physical_devices[0],\n",
        "    [tf.config.LogicalDeviceConfiguration(),\n",
        "     tf.config.LogicalDeviceConfiguration()])\n",
        "\n",
        "tfd = tfp.distributions\n",
        "tfb = tfp.bijectors\n",
        "tfpk = tfp.math.psd_kernels\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import scipy.interpolate\n",
        "import IPython\n",
        "import seaborn as sns\n",
        "from inference_gym import using_tensorflow as gym\n",
        "import logging"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y52jA6ypIQm1"
      },
      "source": [
        "## Bijectors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TMDJbHd1iBY8"
      },
      "source": [
        "### `Glow`\n",
        "\n",
        "A bijector from the paper [Glow: Generative Flow with Invertible 1x1 Convolutions](https://arxiv.org/abs/1807.03039), by Kingma and Dhariwal.\n",
        "\n",
        "Here is how to draw an image from a distribution (note that the distribution has not \"learned\" anything here)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VOR6qU_1jDqR"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "image_shape = (32, 32, 4)  # 32 x 32 RGBA image\n",
        "\n",
        "glow = tfb.Glow(output_shape=image_shape,\n",
        "                coupling_bijector_fn=tfb.GlowDefaultNetwork,\n",
        "                exit_bijector_fn=tfb.GlowDefaultExitNetwork)\n",
        "\n",
        "pz = tfd.Sample(tfd.Normal(0., 1.), tf.reduce_prod(image_shape))\n",
        "\n",
        "# Calling glow on distribution p(z) creates our glow distribution over images.\n",
        "px = glow(pz)\n",
        "\n",
        "# Take samples from the distribution to get images from your dataset.\n",
        "image = px.sample(1)[0].numpy()\n",
        "\n",
        "# Rescale to [0, 1].\n",
        "image = (image - image.min()) / (image.max() - image.min())\n",
        "plt.imshow(image);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lk4QxaPAe7CJ"
      },
      "source": [
        "### `RayleighCDF`\n",
        "\n",
        "Bijector for the [Rayleigh distribution's](https://en.wikipedia.org/wiki/Rayleigh_distribution) CDF. One use is sampling from the Rayleigh distribution, by taking uniform samples, then passing them through the inverse of the CDF."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RKn9hJ-ljTd2"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "bij = tfb.RayleighCDF()\n",
        "uniforms = tfd.Uniform().sample(10_000)\n",
        "plt.hist(bij.inverse(uniforms), bins='auto');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qZMD_bR-hJLc"
      },
      "source": [
        "### `Ascending()` replaces `Invert(Ordered())`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3HpcPlq5A8Xp"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tf.Tensor([1.9363368 2.650928  3.4936204 4.1817293 5.6920815], shape=(5,), dtype=float32)\n",
            "WARNING:tensorflow:From <ipython-input-5-1406b9939c00>:3: Ordered.__init__ (from tensorflow_probability.python.bijectors.ordered) is deprecated and will be removed after 2021-01-09.\n",
            "Instructions for updating:\n",
            "`Ordered` bijector is deprecated; please use `tfb.Invert(tfb.Ascending())` instead.\n",
            "tf.Tensor([1.9363368 2.650928  3.4936204 4.1817293 5.6920815], shape=(5,), dtype=float32)\n"
          ]
        }
      ],
      "source": [
        "x = tfd.Normal(0., 1.).sample(5)\n",
        "print(tfb.Ascending()(x))\n",
        "print(tfb.Invert(tfb.Ordered())(x))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JkLyCi2hkjF3"
      },
      "source": [
        "### Add `low` arg: `Softplus(low=2.)`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "o6vQ8_NgBdjH"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = tf.linspace(-4., 4., 100)\n",
        "\n",
        "for low in (-1., 0., 1.):\n",
        "  bij = tfb.Softplus(low=low)\n",
        "  plt.plot(x, bij(x));"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3ifmOfQ4ISAc"
      },
      "source": [
        "### `tfb.ScaleMatvecLinearOperatorBlock` supports blockwise `LinearOperator`, multi-part args"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "obIBG3aoDDQk"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/linalg/linear_operator_block_diag.py:223: LinearOperator.graph_parents (from tensorflow.python.ops.linalg.linear_operator) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Do not call `graph_parents`.\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "[<tf.Tensor: shape=(3,), dtype=float32, numpy=array([ 1., -2.,  9.], dtype=float32)>,\n",
              " <tf.Tensor: shape=(2,), dtype=float32, numpy=array([5., 3.], dtype=float32)>]"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "op_1 = tf.linalg.LinearOperatorDiag(diag=[1., -1., 3.])\n",
        "op_2 = tf.linalg.LinearOperatorFullMatrix([[12., 5.], [-1., 3.]])\n",
        "scale = tf.linalg.LinearOperatorBlockDiag([op_1, op_2], is_non_singular=True)\n",
        "\n",
        "bij = tfb.ScaleMatvecLinearOperatorBlock(scale)\n",
        "bij([[1., 2., 3.], [0., 1.]])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iHBsq_t5IIQy"
      },
      "source": [
        "## Distributions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oxrTNhcjIFdH"
      },
      "source": [
        "### `Skellam`\n",
        "\n",
        "Distribution over differences of two `Poisson` RVs.   Note that samples from this distribution can be negative."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ahi7o2idEXPT"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = tf.linspace(-5., 10., 10 - -5 + 1)\n",
        "\n",
        "rates = (4, 2)\n",
        "for i, rate in enumerate(rates):\n",
        "  plt.bar(x - .3 * (1 - i), tfd.Poisson(rate).prob(x), label=f'Poisson({rate})', alpha=0.5, width=.3)\n",
        "plt.bar(x.numpy() + .3, tfd.Skellam(*rates).prob(x).numpy(), color='k', alpha=0.25, width=.3,\n",
        "        label=f'Skellam{rates}')\n",
        "\n",
        "plt.legend();"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9BEZCVGdeqbS"
      },
      "source": [
        "### `JointDistributionCoroutine[AutoBatched]` produce `namedtuple`-like samples\n",
        "\n",
        "Explicitly specify `sample_dtype=[...]` for the old `tuple` behavior."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_ZTw_-LyFdSy"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:Note that RandomStandardNormal inside pfor op may not give same output as inside a sequential loop.\n",
            "WARNING:tensorflow:Note that RandomStandardNormal inside pfor op may not give same output as inside a sequential loop.\n"
          ]
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "@tfd.JointDistributionCoroutineAutoBatched\n",
        "def model():\n",
        "  x = yield tfd.Normal(0., 1., name='x')\n",
        "  y = x + 4.\n",
        "  yield tfd.Normal(y, 1., name='y')\n",
        "\n",
        "draw = model.sample(10_000)\n",
        "\n",
        "plt.hist(draw.x, bins='auto', alpha=0.5)\n",
        "plt.hist(draw.y, bins='auto', alpha=0.5);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HQFqtfraeQPm"
      },
      "source": [
        "### `VonMisesFisher` supports `dim > 5`, `entropy()`\n",
        "\n",
        "The [von Mises-Fisher distribution](https://en.wikipedia.org/wiki/Von_Mises%E2%80%93Fisher_distribution) is a distribution on the $n-1$ dimensional sphere in $\\mathbb{R}^n$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KwmpfNJPUQB4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tf.Tensor(3.3533673, shape=(), dtype=float32)\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([1.0000002 , 0.99999994, 1.0000001 ], dtype=float32)>"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "dist = tfd.VonMisesFisher([0., 1, 0, 1, 0, 1], concentration=1.)\n",
        "draws = dist.sample(3)\n",
        "\n",
        "print(dist.entropy())\n",
        "tf.reduce_sum(draws ** 2, axis=1)  # each draw has length 1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m7znpTpzeh1P"
      },
      "source": [
        "### `ExpGamma`, `ExpInverseGamma`\n",
        "\n",
        "`log_rate` parameter added to `Gamma`.\n",
        "Numerical improvements when sampling low-concentration `Beta`, `Dirichlet` & friends. Implicit reparameterization gradients in all cases."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Oc65bs8AHC4M"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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wkfTgVfLfyjPgJgIzI5kHDM4PGt4PmBMRayJiLTCHPrhTs5m1j6a4KtDMWsuYKde8ML1k6kH9WJIXkzQG2A2YDwwvPKrlIWB4nh4JLC28bVlOq5XeeRuTSS1djB49ukflK3539Wq279jManOLlZm1DUmbA1cAnys+vR4g0vO7SnmGV0RMi4jxETF+2LCWvxWXmZXIgZWZtQVJLyUFVRdHxJU5eWXu4iP/XZXTlwOjCm/fLqfVSjczq4sDKzNreZIEXATcFRHnFBbNAipX9k0Cri6kH5mvDtwLeCx3GV4L7CtpSB60vm9OMzOri8dYmVk7eBtwBPA3SbfktFOAqcBlko4B7gcOzctmAwcCi4CngKMBImKNpNOBm3O+r0TEmr75CGbWDhxYmVnLi4g/AqqxeEKV/AEcW2Nd04Hp5ZXOzAYSdwWamZmZlcSBlZmZmVlJHFiZmZmZlcSBlZmZmVlJHFiZmZmZlcSBlZmZmVlJHFiZmZmZlaSuwErS8ZLukHS7pEskbSpprKT5khZJ+rmkjXPeTfL8orx8TCM/gJmZmVmz6DawkjQS+AwwPiJeD2wEHAacBZwbEa8B1gLH5LccA6zN6efmfGZmZmZtr96uwEHAyyQNAl4OrADeA1yel88ADsnTE/M8efmE/BwvMzMzs7bWbWAVEcuBs4EHSAHVY8BC4NGIWJezLQNG5umRwNL83nU5/zblFtvMzMys+dTTFTiE1Ao1FnglsBmw/4ZuWNJkSQskLVi9evWGrs7MzMys39XzEOZ9gL9HxGoASVeSniQ/WNKg3Cq1HbA8518OjAKW5a7DrYBHOq80IqYB0wDGjx8fG/pBzKzxxky5pr+LYGbW1OoZY/UAsJekl+exUhOAO4E/AB/MeSYBV+fpWXmevPz3+UnyZmZmZm2tnjFW80mD0P8C/C2/ZxpwEvB5SYtIY6guym+5CNgmp38emNKAcpuZmZk1nXq6AomIU4FTOyUvBvaokvcZ4EMbXjQzMzOz1lJXYGVmA5vHVpmZ1cePtDEzMzMriQMrMzMzs5I4sDIzMzMriQMrMzMzs5I4sDIzMzMriQMrMzMzs5I4sDIzMzMriQMrMzMzs5I4sDIzMzMriQMrMzMzs5I4sDIzMzMriQMrMzMzs5I4sDIzMzMriQMrM2t5kqZLWiXp9kLaaZKWS7olvw4sLDtZ0iJJ90jar5C+f05bJGlKX38OM2t9DqzMrB38GNi/Svq5EbFrfs0GkLQTcBiwc37PdyVtJGkj4DvAAcBOwEdyXjOzug3q7wKYmW2oiLhR0pg6s08ELo2IZ4G/S1oE7JGXLYqIxQCSLs157yy5uGbWxtxiZWbt7DhJt+WuwiE5bSSwtJBnWU6rlf4ikiZLWiBpwerVqxtRbjNrUQ6szKxdXQi8GtgVWAF8s6wVR8S0iBgfEeOHDRtW1mrNrA24K9DM2lJErKxMS/oB8Os8uxwYVci6XU6ji3Qzs7q4xcrM2pKkEYXZ9wOVKwZnAYdJ2kTSWGAccBNwMzBO0lhJG5MGuM/qyzKbWetzi5WZtTxJlwB7A0MlLQNOBfaWtCsQwBLgEwARcYeky0iD0tcBx0bEv/J6jgOuBTYCpkfEHX38UcysxTmwMrOWFxEfqZJ8URf5zwDOqJI+G5hdYtHMbIBxV6CZmZlZSRxYmZmZmZXEXYFmVtWYKdf0dxHMzFpOXS1WkgZLulzS3ZLukvQWSVtLmiPp3vx3SM4rSefnZ23dJmn3xn4EMzMzs+ZQb1fgecBvI+K1wC7AXcAU4PqIGAdcn+chPWdrXH5NJt2kz8zMzKztddsVKGkr4J3AUQAR8RzwnKSJpMubAWYAc4GTSM/WmhkRAczLrV0jImJF6aU3s9L1tAuwkn/J1IMaURwzs5ZST4vVWGA18CNJf5X0Q0mbAcMLwdJDwPA8XffztszMzMzaST2B1SBgd+DCiNgN+Afru/0AyK1T0ZMN+yGmZmZm1m7qCayWAcsiYn6ev5wUaK2sPDIi/12Vl3f1HK4X+CGmZmZm1m66Dawi4iFgqaQdc9IE0qMgZgGTctok4Oo8PQs4Ml8duBfwmMdXmZmZ2UBQ732sPg1cnB9Muhg4mhSUXSbpGOB+4NCcdzZwILAIeCrnNTMzM2t7dQVWEXELML7KoglV8gZw7AaWy8zMzKzl+JE2ZmZmZiVxYGVmZmZWEgdWZmZmZiXxQ5jNDPBDl83MyuAWKzMzM7OSOLAyMzMzK4kDKzMzM7OSOLAyMzMzK4kDKzMzM7OSOLAyMzMzK4kDKzMzM7OSOLAyMzMzK4kDKzMzM7OSOLAyMzMzK4kDKzMzM7OS+FmBZgOYnw9oZlYut1iZmZmZlcSBlZmZmVlJHFiZWcuTNF3SKkm3F9K2ljRH0r3575CcLknnS1ok6TZJuxfeMynnv1fSpP74LGbW2hxYmVk7+DGwf6e0KcD1ETEOuD7PAxwAjMuvycCFkAIx4FRgT2AP4NRKMGZmVi8HVmbW8iLiRmBNp+SJwIw8PQM4pJA+M5J5wGBJI4D9gDkRsSYi1gJzeHGwZmbWJQdWZtauhkfEijz9EDA8T48ElhbyLctptdJfRNJkSQskLVi9enW5pTazlubAyszaXkQEECWub1pEjI+I8cOGDStrtWbWBnwfK7MBaIDcv2qlpBERsSJ39a3K6cuBUYV82+W05cDendLn9kE5zayNuMXKbAAZM+WagRJUAcwCKlf2TQKuLqQfma8O3At4LHcZXgvsK2lIHrS+b04zM6ubW6zMrOVJuoTU2jRU0jLS1X1TgcskHQPcDxyas88GDgQWAU8BRwNExBpJpwM353xfiYjOA+LNzLpUd2AlaSNgAbA8It4raSxwKbANsBA4IiKek7QJMBN4E/AI8OGIWFJ6yc3Msoj4SI1FE6rkDeDYGuuZDkwvsWhmNsD0pCvws8BdhfmzgHMj4jXAWuCYnH4MsDann5vzmZmZmbW9ulqsJG0HHAScAXxekoD3AB/NWWYAp5FutDcxTwNcDlwgSflXopmZmVndejMudMnUgxpQkvrU22L1LeBE4Pk8vw3waESsy/PF+728cC+YvPyxnL8D3wfGzMzM2k23gZWk9wKrImJhmRv2fWDMzMys3dTTFfg24H2SDgQ2BbYEziM9BmJQbpWq3AcG1t8jZpmkQcBWpEHsZmZmZm2t2xariDg5IraLiDHAYcDvI+Jw4A/AB3O2zveIqdw75oM5v8dXmZmZWdvbkBuEnkQayL6INIbqopx+EbBNTv88658ob2ZmZtbWenSD0IiYS37EQ0QsBvaokucZ4EMllM3MSjCA7rRuZtbv/EgbMzMzs5I4sDIzMzMriZ8VaGZmZn1iIAxNcIuVmZmZWUkcWJmZmZmVxF2BZm1qIDS5m5k1G7dYmZmZmZXEgZWZmZlZSRxYmZmZmZXEgZWZmZlZSRxYmZmZmZXEVwWamZlZj/nK4+rcYmVmZmZWErdYmZmZDXBufSqPW6zMzMzMSuIWKzMzszbjFqj+48DKrA24EjUzaw4OrMxamAMqM7Pm4jFWZmZmZiVxYGVmZmZWEncFmpmZWVvpzTCJJVMPKmXbbrEys7YmaYmkv0m6RdKCnLa1pDmS7s1/h+R0STpf0iJJt0navX9Lb2atxi1WZjYQvDsiHi7MTwGuj4ipkqbk+ZOAA4Bx+bUncGH+a9ZvfJFKa3GLlZkNRBOBGXl6BnBIIX1mJPOAwZJG9EcBzaw1ObAys3YXwHWSFkqanNOGR8SKPP0QMDxPjwSWFt67LKeZmdXFXYFm1u7eHhHLJW0LzJF0d3FhRISk6MkKc4A2GWD06NHlldTMWl63gZWkUcBM0i+6AKZFxHmStgZ+DowBlgCHRsRaSQLOAw4EngKOioi/NKb4ZmZdi4jl+e8qSVcBewArJY2IiBW5q29Vzr4cGFV4+3Y5rfM6pwHTAMaPH9+joMwGNo+Xan/1dAWuA06IiJ2AvYBjJe3E+sGf44Dr8zx0HPw5mTT408x6acyUa1wZ95KkzSRtUZkG9gVuB2YBk3K2ScDVeXoWcGS+OnAv4LFCl6GZWbe6bbHKlcqKPP2EpLtIYw4mAnvnbDOAuaSral4Y/AnMkzS48suw/OKbmXVpOHBVakhnEPCziPitpJuByyQdA9wPHJrzzya1ti8itbgf3fdFNrNW1qMxVpLGALsB8+n54M8OgZXHKJj1nluw6hMRi4FdqqQ/Akyokh7AsX1QNGsDPg6tmrqvCpS0OXAF8LmIeLy4LFdGPRpnEBHTImJ8RIwfNmxYT95qZmZm1pTqCqwkvZQUVF0cEVfm5JWV+7v0ZvCnmZmZWbup56pAARcBd0XEOYVFlcGfU3nx4M/jJF1KumOxB3+alcDdDmZmza+eMVZvA44A/ibplpx2Cimg8uBPMzNref7hYmWp56rAPwKqsdiDP83MzMwy33ndzMzajlugrL/4WYFmZmZmJXGLlVkT8q9tM7PW5BYrMzMzs5K4xcrMzJqaW3CtlTiwMmsCPnGYmbUHdwWamZmZlcQtVmZm1mfcOmvtzi1WZmZmZiVxi5WZmbklyawkDqzMGqh4sloy9aCay8zMrD04sDLrIw6kzMzanwMrM7M25EDerH948LqZmZlZSdxiZWbW5Nz6ZNY6HFiZlcgnQDOzgc1dgWZmZmYlcWBlZmZmVhIHVmZmZmYl8RgrszpUu9Gnx1OZmVlnbrEyMzMzK4lbrMy6UK1Vyi1VZmZWiwMrs6yr5/qZmZnVw4GVDUgOoszMrBEcWFnbqnfAubv7zMysLA0ZvC5pf0n3SFokaUojtmFm1iiuw8yst0pvsZK0EfAd4N+AZcDNkmZFxJ1lb8usGrdA2YZwHWZmG6IRXYF7AIsiYjGApEuBiYArpQGgEsAUxy1VS+u8rBrfL8r6ieswM+u1RgRWI4GlhfllwJ4N2E5bKGMQdU+Dk74IWMpoNXJAZf3EdZiZ9Vq/DV6XNBmYnGeflHRPHW8bCjzcuFI1TF3l1lnlb7jaOnu4nbb+zptQy5ZbZ/W43Ns3pCR9oJf1VyO06v5Siz9Pc2vrz9PDc2PN+qsRgdVyYFRhfruc1kFETAOm9WTFkhZExPgNK17fa9VyQ+uW3eXuW61a7hq6rcN6U381Qpt97/48Tc6fpz6NuCrwZmCcpLGSNgYOA2Y1YDtmZo3gOszMeq30FquIWCfpOOBaYCNgekTcUfZ2zMwawXWYmW2IhoyxiojZwOwGrLrfm957qVXLDa1bdpe7b7VquatqYB1Wtrb63vHnaXb+PHVQRDRivWZmZmYDTkPuvG5mZmY2EDVtYCXpNEnLJd2SXwcWlp2cHzVxj6T9CulN8xgKSSdICklD87wknZ/Ldpuk3Qt5J0m6N78m9VN5T8/lukXSdZJe2SLl/oaku3PZrpI0uLCsqfcTSR+SdIek5yWN77Ssqcte1IxlaneSdpU0Lx+vCyTtkdNrHq/NTtKn87F8h6SvF9KrHgutoCfngWbVmzq22TW8zoqIpnwBpwH/WSV9J+BWYBNgLHAfaYDpRnn6VcDGOc9O/VT2UaSBr/cDQ3PagcBvAAF7AfNz+tbA4vx3SJ4e0g9l3rIw/Rngey1S7n2BQXn6LOCsFtpPXgfsCMwFxrfSPl4oa9OVaSC8gOuAA/L0gcDcwvSLjtdmfwHvBn4HbJLnt81/qx4L/V3eOj9T3eeBZn71tI7t7/LW8XkaXmc1bYtVFyYCl0bEsxHxd2AR6REULzyGIiKeAyqPoegP5wInAsUBbBOBmZHMAwZLGgHsB8yJiDURsRaYA+zf1wWOiMcLs5uxvuzNXu7rImJdnp1HuudQpdxNvZ9ExF0RUe3Gkk1f9oJmLNNAEMCWeXor4ME8Xet4bXafAqZGxLMAEbEqp9c6FlpBT84DTasXdWyza3id1eyB1XG5+XG6pCE5rdrjJkZ2kd6nJE0ElkfErZ0WNXW5ASSdIWkpcDjwpZzc9OUu+Djp1yC0Vrk7a6WyN2OZBoLPAd/Ix+vZwMk5vVX/HzsA75A0X9INkt6c01vy8/TiPNAq6qljm13Dy91vj7QBkPQ74BVVFn0BuBA4nRTtnw58k/RP7XfdlPsUUtNp0+mq3BFxdUR8AfiCpJOB44BT+7SANXRX7ik8zogAAAJFSURBVJznC8A64OK+LFt36im7WTXd1DMTgOMj4gpJhwIXAfv0Zfl6qpvPM4g0rGAv4M3AZZJe1YfF67FWPQ9U08p1bDPq18AqIuqqCCT9APh1nu3qcRPdPkqnDLXKLekNpL7mWyVVyvCXPLC0VrmXA3t3Sp9beqGp//smHTizSYFV05db0lHAe4EJkTvRaYL9BHr0nRc1RdnrVNcjrKznutp3JM0EPptnfwH8ME837f+jm8/zKeDKfPzeJOl50nPcWu7z9PI80K8aUMc2s8aXu78HktV6ASMK08eT+nIBdqbjgLnFpMFog/L0WNYPSNu5nz/DEtYPWjyIjoMWb8rpWwN/Jw0AH5Knt+6Hso4rTH8auLxFyr0/cCcwrFN6K+0nc+k4eL2Vyt50ZRoIL+AuYO88PQFYmKerHq/N/gI+CXwlT+9A6qpRrWOhv8vbw8/W7XmgmV89rWP7u7x1fJ6G11n92mLVja9L2pXUFbgE+ARARNwh6TLSP3odcGxE/AtAzf0YitmkK0IWAU8BRwNExBpJp5OeTwapclnTD+WbKmlH4HnSVSyfzOnNXu4LSAf2nPzrcF5EfLIV9hNJ7we+DQwDrpF0S0Ts1wplrwg//qW//AdwnqRBwDPA5Jxe9XhtAdOB6ZJuB54DJkU6C9Y8FlpUK/5/elzHNrO+qLN853UzMzOzkjT7VYFmZmZmLcOBlZmZmVlJHFiZmZmZlcSBlZmZmVlJHFiZmZmZlcSBlZmZmVlJHFiZmZmZlcSBlZmZmVlJ/hfRuUL9lNHFoQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(10, 3))\n",
        "plt.subplot(121)\n",
        "plt.hist(tfd.Beta(.02, .02).sample(10_000), bins='auto')\n",
        "plt.title('Beta(.02, .02)')\n",
        "plt.subplot(122)\n",
        "plt.title('GamX/(GamX+GamY) [the old way]')\n",
        "g = tfd.Gamma(.02, 1); s0, s1 = g.sample(10_000), g.sample(10_000)\n",
        "plt.hist(s0 / (s0 + s1), bins='auto')\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=(10, 3))\n",
        "plt.subplot(121)\n",
        "plt.hist(tfd.ExpGamma(.02, 1.).sample(10_000), bins='auto')\n",
        "plt.title('ExpGamma(.02, 1)')\n",
        "plt.subplot(122)\n",
        "plt.hist(tfb.Log()(tfd.Gamma(.02, 1.)).sample(10_000), bins='auto')\n",
        "plt.title('tfb.Log()(Gamma(.02, 1)) [the old way]');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dFxOLc-dICrZ"
      },
      "source": [
        "### `JointDistribution*AutoBatched` support reproducible sampling (with length-2 tuple/Tensor seeds)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "g_JiQHJKJx2X"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "StructTuple(\n",
            "  x=<tf.Tensor: shape=(), dtype=float32, numpy=-0.59835213>,\n",
            "  y=<tf.Tensor: shape=(), dtype=float32, numpy=6.2380724>\n",
            ")\n",
            "StructTuple(\n",
            "  x=<tf.Tensor: shape=(), dtype=float32, numpy=-0.59835213>,\n",
            "  y=<tf.Tensor: shape=(), dtype=float32, numpy=6.2380724>\n",
            ")\n"
          ]
        }
      ],
      "source": [
        "@tfd.JointDistributionCoroutineAutoBatched\n",
        "def model():\n",
        "  x = yield tfd.Normal(0, 1, name='x')\n",
        "  y = yield tfd.Normal(x + 4, 1, name='y')\n",
        "\n",
        "print(model.sample(seed=(1, 2)))\n",
        "print(model.sample(seed=(1, 2)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XC5X2xv5i1wH"
      },
      "source": [
        "### `KL(VonMisesFisher || SphericalUniform)`\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uuTMyfVbJ-_2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tf.Tensor([4.7683716e-07 4.9877167e-04 4.9384594e-02 2.4844694e+00], shape=(4,), dtype=float32)\n"
          ]
        }
      ],
      "source": [
        "# Build vMFs with the same mean direction, batch of increasing concentrations.\n",
        "vmf = tfd.VonMisesFisher(tf.math.l2_normalize(tf.random.normal([10])),\n",
        "                         concentration=[0., .1, 1., 10.])\n",
        "# KL increases with concentration, since vMF(conc=0) == SphericalUniform.\n",
        "print(tfd.kl_divergence(vmf, tfd.SphericalUniform(10)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H8HHW-gaJC6i"
      },
      "source": [
        "### `parameter_properties`\n",
        "\n",
        "Distribution classes now expose a `parameter_properties(dtype=tf.float32, num_classes=None)` class method, which can enable automated construction of many classes of distributions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "THkRIhYlKulZ"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gamma: {'concentration': ParameterProperties(event_ndims=0, shape_fn=<function ParameterProperties.<lambda> at 0x7ff6bbfcdd90>, default_constraining_bijector_fn=<function Gamma._parameter_properties.<locals>.<lambda> at 0x7ff6afd95510>, is_preferred=True), 'rate': ParameterProperties(event_ndims=0, shape_fn=<function ParameterProperties.<lambda> at 0x7ff6bbfcdd90>, default_constraining_bijector_fn=<function Gamma._parameter_properties.<locals>.<lambda> at 0x7ff6afd95ea0>, is_preferred=False), 'log_rate': ParameterProperties(event_ndims=0, shape_fn=<function ParameterProperties.<lambda> at 0x7ff6bbfcdd90>, default_constraining_bijector_fn=<class 'tensorflow_probability.python.bijectors.identity.Identity'>, is_preferred=True)}\n",
            "Categorical: {'logits': ParameterProperties(event_ndims=1, shape_fn=<function Categorical._parameter_properties.<locals>.<lambda> at 0x7ff6afd95510>, default_constraining_bijector_fn=<class 'tensorflow_probability.python.bijectors.identity.Identity'>, is_preferred=True), 'probs': ParameterProperties(event_ndims=1, shape_fn=<function Categorical._parameter_properties.<locals>.<lambda> at 0x7ff6afdc91e0>, default_constraining_bijector_fn=<class 'tensorflow_probability.python.bijectors.softmax_centered.SoftmaxCentered'>, is_preferred=False)}\n"
          ]
        }
      ],
      "source": [
        "print('Gamma:', tfd.Gamma.parameter_properties())\n",
        "print('Categorical:', tfd.Categorical.parameter_properties(dtype=tf.float64, num_classes=7))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9qMds4htI1Nl"
      },
      "source": [
        "### `experimental_default_event_space_bijector`\n",
        "\n",
        "Now accepts additional args pinning some distribution parts."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "t1WzLvieLFsI"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "StructTuple(\n",
              "  scale=<tf.Tensor: shape=(3,), dtype=float32, numpy=array([0.6630705, 1.5401832, 1.0777743], dtype=float32)>\n",
              ")"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "@tfd.JointDistributionCoroutineAutoBatched\n",
        "def model():\n",
        "  scale = yield tfd.Gamma(1, 1, name='scale')\n",
        "  obs = yield tfd.Normal(0, scale, name='obs')\n",
        "\n",
        "model.experimental_default_event_space_bijector(obs=.2).forward(\n",
        "    [tf.random.uniform([3], -2, 2.)])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZIvOfH61I6cR"
      },
      "source": [
        "### `JointDistribution.experimental_pin`\n",
        "\n",
        "Pins some joint distribution parts, returning `JointDistributionPinned` object representing the joint unnormalized density. \n",
        "\n",
        "Working with the `experimental_default_event_space_bijector`, this makes doing variational inference or MCMC with sensible defaults much more straightforward. In the below example, the first two lines of `sample` make running MCMC a breeze."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "olBsLx1TLk8F"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "dist = tfd.JointDistributionSequential([\n",
        "    tfd.HalfNormal(1.),\n",
        "    lambda scale: tfd.Normal(0., scale, name='observed')])\n",
        "\n",
        "@tf.function\n",
        "def sample():\n",
        "  bij = dist.experimental_default_event_space_bijector(observed=1.)\n",
        "  target_log_prob = dist.experimental_pin(observed=1.).unnormalized_log_prob\n",
        "\n",
        "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
        "      tfp.mcmc.HamiltonianMonteCarlo(target_log_prob,\n",
        "                                     step_size=0.6,\n",
        "                                     num_leapfrog_steps=16),\n",
        "      bijector=bij)\n",
        "  return tfp.mcmc.sample_chain(500, \n",
        "                               current_state=tf.ones([8]),  # multiple chains\n",
        "                               kernel=kernel,\n",
        "                               trace_fn=None)\n",
        "\n",
        "draws = sample()\n",
        "\n",
        "fig, (hist, trace) = plt.subplots(ncols=2, figsize=(16, 3))\n",
        "trace.plot(draws, alpha=0.5)\n",
        "for col in tf.transpose(draws):\n",
        "  sns.kdeplot(col, ax=hist);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ep-jMPbcdpnT"
      },
      "source": [
        "### `tfd.NegativeBinomial.experimental_from_mean_dispersion`\n",
        "Alternative parameterization. Email tfprobability@tensorflow.org or send us a PR to add similar class methods for other distributions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Jd00nlZLMFsC"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "nb = tfd.NegativeBinomial.experimental_from_mean_dispersion(30., .01)\n",
        "plt.hist(nb.sample(10_000), bins='auto');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "POhRZPKij_Ik"
      },
      "source": [
        "### `tfp.experimental.distribute`\n",
        "\n",
        "`DistributionStrategy`-aware joint distributions, allowing for cross-device likelihood computations. Sharded `Independent` and `Sample` distributions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZBsGV8myd_pO"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:There are non-GPU devices in `tf.distribute.Strategy`, not using nccl allreduce.\n",
            "INFO:tensorflow:Using MirroredStrategy with devices ('/job:localhost/replica:0/task:0/device:CPU:0', '/job:localhost/replica:0/task:0/device:CPU:1')\n",
            "\n",
            "Note that the global latent `group_scale` is shared across devices, whereas \n",
            "the local `x` is sampled independently on each device.\n",
            "\n",
            "sample: StructTuple(\n",
            "  group_scale=PerReplica:{\n",
            "      0: <tf.Tensor: shape=(3,), dtype=float32, numpy=array([2.6355493, 1.1805456, 1.245112 ], dtype=float32)>,\n",
            "      1: <tf.Tensor: shape=(3,), dtype=float32, numpy=array([2.6355493, 1.1805456, 1.245112 ], dtype=float32)>\n",
            "    },\n",
            "  x=PerReplica:{\n",
            "      0: <tf.Tensor: shape=(2, 3), dtype=float32, numpy=\n",
            "    array([[-0.90548456,  0.7675636 ,  0.27627748],\n",
            "           [-0.3475989 ,  2.0194046 , -1.2531326 ]], dtype=float32)>,\n",
            "      1: <tf.Tensor: shape=(2, 3), dtype=float32, numpy=\n",
            "    array([[ 3.251305  , -0.5790973 ,  0.42745453],\n",
            "           [-1.562331  ,  0.3006323 ,  0.635732  ]], dtype=float32)>\n",
            "    }\n",
            ")\n",
            "another sample: StructTuple(\n",
            "  group_scale=PerReplica:{\n",
            "      0: <tf.Tensor: shape=(3,), dtype=float32, numpy=array([2.41133   , 0.10307606, 0.5236566 ], dtype=float32)>,\n",
            "      1: <tf.Tensor: shape=(3,), dtype=float32, numpy=array([2.41133   , 0.10307606, 0.5236566 ], dtype=float32)>\n",
            "    },\n",
            "  x=PerReplica:{\n",
            "      0: <tf.Tensor: shape=(2, 3), dtype=float32, numpy=\n",
            "    array([[-3.2476294 ,  0.07213175, -0.39536062],\n",
            "           [-1.2319602 , -0.05505352,  0.06356457]], dtype=float32)>,\n",
            "      1: <tf.Tensor: shape=(2, 3), dtype=float32, numpy=\n",
            "    array([[ 5.6028705 ,  0.11919801, -0.48446828],\n",
            "           [-1.5938259 ,  0.21123725,  0.28979057]], dtype=float32)>\n",
            "    }\n",
            ")\n",
            "\n",
            "Note that each device observes the same log_prob (local latent log_probs are\n",
            "summed across devices).\n",
            "\n",
            "INFO:tensorflow:Reduce to /job:localhost/replica:0/task:0/device:CPU:0 then broadcast to ('/job:localhost/replica:0/task:0/device:CPU:0', '/job:localhost/replica:0/task:0/device:CPU:1').\n",
            "log_prob: PerReplica:{\n",
            "  0: tf.Tensor(-25.05747, shape=(), dtype=float32),\n",
            "  1: tf.Tensor(-25.05747, shape=(), dtype=float32)\n",
            "}\n",
            "\n",
            "Note that each device observes the same log_prob gradient (local latents have\n",
            "independent gradients, global latents are aggregated across devices).\n",
            "\n",
            "INFO:tensorflow:Reduce to /job:localhost/replica:0/task:0/device:CPU:0 then broadcast to ('/job:localhost/replica:0/task:0/device:CPU:0', '/job:localhost/replica:0/task:0/device:CPU:1').\n",
            "INFO:tensorflow:Reduce to /job:localhost/replica:0/task:0/device:CPU:0 then broadcast to ('/job:localhost/replica:0/task:0/device:CPU:0', '/job:localhost/replica:0/task:0/device:CPU:1').\n",
            "grad_log_prob: StructTuple(\n",
            "  group_scale=PerReplica:{\n",
            "      0: <tf.Tensor: shape=(3,), dtype=float32, numpy=array([-1.7555585, -1.2928739, -3.0554674], dtype=float32)>,\n",
            "      1: <tf.Tensor: shape=(3,), dtype=float32, numpy=array([-1.7555585, -1.2928739, -3.0554674], dtype=float32)>\n",
            "    },\n",
            "  x=PerReplica:{\n",
            "      0: <tf.Tensor: shape=(2, 3), dtype=float32, numpy=\n",
            "    array([[ 0.13035832, -0.5507428 , -0.17820862],\n",
            "           [ 0.05004217, -1.4489648 ,  0.80831426]], dtype=float32)>,\n",
            "      1: <tf.Tensor: shape=(2, 3), dtype=float32, numpy=\n",
            "    array([[-0.46807498,  0.41551432, -0.27572307],\n",
            "           [ 0.22492138, -0.21570992, -0.41006932]], dtype=float32)>\n",
            "    }\n",
            ")\n"
          ]
        }
      ],
      "source": [
        "# Note: 2-logical devices are configured in the install/import cell at top.\n",
        "strategy = tf.distribute.MirroredStrategy()\n",
        "assert strategy.num_replicas_in_sync == 2\n",
        "\n",
        "@tfp.experimental.distribute.JointDistributionCoroutine\n",
        "def model():\n",
        "  root = tfp.experimental.distribute.JointDistributionCoroutine.Root\n",
        "  group_scale = yield root(tfd.Sample(tfd.Exponential(1), 3, name='group_scale'))\n",
        "  _ = yield tfp.experimental.distribute.ShardedSample(tfd.Independent(tfd.Normal(0, group_scale), 1),\n",
        "                                                      sample_shape=[4], name='x')\n",
        "\n",
        "seed1, seed2 = tfp.random.split_seed((1, 2))\n",
        "\n",
        "@tf.function\n",
        "def sample(seed):\n",
        "  return model.sample(seed=seed)\n",
        "xs = strategy.run(sample, (seed1,))\n",
        "print(\"\"\"\n",
        "Note that the global latent `group_scale` is shared across devices, whereas\n",
        "the local `x` is sampled independently on each device.\n",
        "\"\"\")\n",
        "print('sample:', xs)\n",
        "print('another sample:', strategy.run(sample, (seed2,)))\n",
        "\n",
        "@tf.function\n",
        "def log_prob(x):\n",
        "  return model.log_prob(x)\n",
        "print(\"\"\"\n",
        "Note that each device observes the same log_prob (local latent log_probs are\n",
        "summed across devices).\n",
        "\"\"\")\n",
        "print('log_prob:', strategy.run(log_prob, (xs,)))\n",
        "\n",
        "@tf.function\n",
        "def grad_log_prob(x):\n",
        "  return tfp.math.value_and_gradient(model.log_prob, x)[1]\n",
        "\n",
        "print(\"\"\"\n",
        "Note that each device observes the same log_prob gradient (local latents have\n",
        "independent gradients, global latents have gradients aggregated across devices).\n",
        "\"\"\")\n",
        "print('grad_log_prob:', strategy.run(grad_log_prob, (xs,)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FtXowbF7IKKr"
      },
      "source": [
        "## PSD Kernels"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FMK3QMjYIN75"
      },
      "source": [
        "### `GeneralizedMatern`\n",
        "\n",
        "The `GeneralizedMatern` positive-semidefinite kernel generalizes `MaternOneHalf`, `MAterhThreeHalves`, and `MaternFiveHalves`.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "R5Ze11XFtHoi"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "gm = tfpk.GeneralizedMatern(df=[0.5, 1.5, 2.5], length_scale=1., amplitude=0.5)\n",
        "m1 = tfpk.MaternOneHalf(length_scale=1., amplitude=0.5)\n",
        "m2 = tfpk.MaternThreeHalves(length_scale=1., amplitude=0.5)\n",
        "m3 = tfpk.MaternFiveHalves(length_scale=1., amplitude=0.5)\n",
        "xs = tf.linspace(-1.5, 1.5, 100)\n",
        "\n",
        "gm_matrix = gm.matrix([[0.]], xs[..., tf.newaxis])\n",
        "plt.plot(xs, gm_matrix[0][0])\n",
        "plt.plot(xs, m1.matrix([[0.]], xs[..., tf.newaxis])[0])\n",
        "plt.show()\n",
        "plt.plot(xs, gm_matrix[1][0])\n",
        "plt.plot(xs, m2.matrix([[0.]], xs[..., tf.newaxis])[0])\n",
        "plt.show()\n",
        "plt.plot(xs, gm_matrix[2][0])\n",
        "plt.plot(xs, m3.matrix([[0.]], xs[..., tf.newaxis])[0])\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K04waYMLIL2c"
      },
      "source": [
        "### `Parabolic` (Epanechnikov)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "C4T8jq2oONow"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "epa = tfpk.Parabolic()\n",
        "xs = tf.linspace(-1.05, 1.05, 100)\n",
        "plt.plot(xs, epa.matrix([[0.]], xs[..., tf.newaxis])[0]);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nXyY5bgLIyrf"
      },
      "source": [
        "## VI\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LYuJ0bqUpSmI"
      },
      "source": [
        "### `build_asvi_surrogate_posterior`\n",
        "Automatically construct a structured surrogate posterior for VI in a way that incorporates the graphical structure of the prior distribution. This utilizes the method described in the paper Automatic Structured Variational Inference (https://arxiv.org/abs/2002.00643)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Hjv8snlYm7Gi"
      },
      "outputs": [],
      "source": [
        "# Import a Brownian Motion model from TFP's inference gym.\r\n",
        "model = gym.targets.BrownianMotionMissingMiddleObservations()\r\n",
        "prior = model.prior_distribution()\r\n",
        "ground_truth = ground_truth = model.sample_transformations['identity'].ground_truth_mean\r\n",
        "target_log_prob = lambda *values: model.log_likelihood(values) + prior.log_prob(values)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3FaLKGHt9BWq"
      },
      "source": [
        "This models a Brownian Motion process with a Gaussian observation model. It consists of 30 timesteps, but the middle 10 timesteps are unobservable.\r\n",
        "\r\n",
        "  ```\r\n",
        "  locs[0] ~ Normal(loc=0, scale=innovation_noise_scale)\r\n",
        "  for t in range(1, num_timesteps):\r\n",
        "    locs[t] ~ Normal(loc=locs[t - 1], scale=innovation_noise_scale)\r\n",
        "\r\n",
        "  for t in range(num_timesteps):\r\n",
        "    observed_locs[t] ~ Normal(loc=locs[t], scale=observation_noise_scale)\r\n",
        "  ```\r\n",
        "\r\n",
        " The goal is to infer the values of `locs` from noisy observations (`observed_locs`). Since the middle 10 timesteps are unobservable, `observed_locs` are `NaN` values at timesteps [10,19]. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UvYo9s0Ss_6K"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# The observed loc values in the Brownian Motion inference gym model\r\n",
        "OBSERVED_LOC = np.array([\r\n",
        "    0.21592641, 0.118771404, -0.07945447, 0.037677474, -0.27885845, -0.1484156,\r\n",
        "    -0.3250906, -0.22957903, -0.44110894, -0.09830782, np.nan, np.nan, np.nan,\r\n",
        "    np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, -0.8786016,\r\n",
        "    -0.83736074, -0.7384849, -0.8939254, -0.7774566, -0.70238715, -0.87771565,\r\n",
        "    -0.51853573, -0.6948214, -0.6202789\r\n",
        "]).astype(dtype=np.float32)\r\n",
        "\r\n",
        "# Plot the prior and the likelihood observations\r\n",
        "plt.figure()\r\n",
        "plt.title('Brownian Motion Prior Samples and Observations')\r\n",
        "\r\n",
        "num_samples = 15\r\n",
        "prior_samples = prior.sample(num_samples)\r\n",
        "\r\n",
        "plt.plot(prior_samples, c='blue', alpha=0.1)\r\n",
        "plt.plot(prior_samples[0][0], label=\"Prior Samples\", c='blue', alpha=0.1)\r\n",
        "\r\n",
        "plt.scatter(x=range(30),y=OBSERVED_LOC, c='black', alpha=0.5, label=\"Observations\")\r\n",
        "\r\n",
        "plt.legend(bbox_to_anchor=(1.05, 1), borderaxespad=0.);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "g1iSSYX-nCLT"
      },
      "outputs": [],
      "source": [
        "logging.getLogger('tensorflow').setLevel(logging.ERROR)  # suppress pfor warnings\r\n",
        "\r\n",
        "# Construct and train an ASVI Surrogate Posterior.\r\n",
        "asvi_surrogate_posterior = tfp.experimental.vi.build_asvi_surrogate_posterior(prior)\r\n",
        "\r\n",
        "asvi_losses = tfp.vi.fit_surrogate_posterior(target_log_prob,\r\n",
        "                                        asvi_surrogate_posterior,\r\n",
        "                                        optimizer=tf.optimizers.Adam(learning_rate=0.1),\r\n",
        "                                        num_steps=500)\r\n",
        "logging.getLogger('tensorflow').setLevel(logging.NOTSET)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sFmuRAt1Czvr"
      },
      "outputs": [],
      "source": [
        "# Construct and train a Mean-Field Surrogate Posterior.\r\n",
        "factored_surrogate_posterior = tfp.experimental.vi.build_factored_surrogate_posterior(event_shape=prior.event_shape)\r\n",
        "\r\n",
        "factored_losses = tfp.vi.fit_surrogate_posterior(target_log_prob,\r\n",
        "                                        factored_surrogate_posterior,\r\n",
        "                                        optimizer=tf.optimizers.Adam(learning_rate=0.1),\r\n",
        "                                        num_steps=500)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GJPtYZAspk8x"
      },
      "outputs": [],
      "source": [
        "logging.getLogger('tensorflow').setLevel(logging.ERROR)  # suppress pfor warnings\r\n",
        "\r\n",
        "# Sample from the posteriors.\r\n",
        "asvi_posterior_samples = asvi_surrogate_posterior.sample(num_samples)\r\n",
        "factored_posterior_samples = factored_surrogate_posterior.sample(num_samples)\r\n",
        "\r\n",
        "logging.getLogger('tensorflow').setLevel(logging.NOTSET)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cmh6F5-_Gsk1"
      },
      "source": [
        "Both the ASVI and the mean-field surrogate posterior distributions have converged, and the ASVI surrogate posterior had a lower final loss (negative ELBO value)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jkqeoRp6EW_o"
      },
      "outputs": [
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot the loss curves.\r\n",
        "plt.figure()\r\n",
        "plt.title('Loss Curves for ASVI vs Mean-Field Surrogate Posteriors')\r\n",
        "\r\n",
        "plt.plot(asvi_losses, c='orange', label='ASVI', alpha = 0.4)\r\n",
        "plt.plot(factored_losses, c='green', label='Mean-Field', alpha = 0.4)\r\n",
        "plt.ylim(-50, 300)\r\n",
        "\r\n",
        "plt.legend(bbox_to_anchor=(1.3, 1), borderaxespad=0.);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hnAw2exeJlqK"
      },
      "source": [
        "The samples from the posteriors highlight how nicely the ASVI surrogate posterior captures the uncertainty for the timesteps without observations. On the other hand, the mean-field surrogate posterior struggles to capture the true uncertainty."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WyBChOi3nIoe"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot samples from the ASVI and Mean-Field Surrogate Posteriors.\r\n",
        "plt.figure()\r\n",
        "plt.title('Posterior Samples from ASVI vs Mean-Field Surrogate Posterior')\r\n",
        "\r\n",
        "plt.plot(asvi_posterior_samples, c='orange', alpha = 0.25)\r\n",
        "plt.plot(asvi_posterior_samples[0][0], label='ASVI Surrogate Posterior', c='orange', alpha = 0.25)\r\n",
        "\r\n",
        "plt.plot(factored_posterior_samples, c='green', alpha = 0.25)\r\n",
        "plt.plot(factored_posterior_samples[0][0], label='Mean-Field Surrogate Posterior', c='green', alpha = 0.25)\r\n",
        "\r\n",
        "plt.scatter(x=range(30),y=OBSERVED_LOC, c='black', alpha=0.5, label='Observations')\r\n",
        "\r\n",
        "plt.plot(ground_truth, c='black', label='Ground Truth')\r\n",
        "\r\n",
        "plt.legend(bbox_to_anchor=(1.585, 1), borderaxespad=0.);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FUx2oXURd3nE"
      },
      "source": [
        "## MCMC"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ywSBLf0Kd-Gd"
      },
      "source": [
        "### `ProgressBarReducer`\n",
        "Visualize progress of the sampler. (May have a nominal performance penalty; not currently supported under JIT compilation.)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-SJjFpd4eW_e"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            " 99%|█████████▉| 99/100 [00:03<00:00, 27.37it/s]\n"
          ]
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "kernel = tfp.mcmc.HamiltonianMonteCarlo(lambda x: -x**2 / 2, .05, 20)\n",
        "pbar = tfp.experimental.mcmc.ProgressBarReducer(100)\n",
        "kernel = tfp.experimental.mcmc.WithReductions(kernel, pbar)\n",
        "plt.hist(tf.reshape(tfp.mcmc.sample_chain(100, current_state=tf.ones([128]), kernel=kernel, trace_fn=None), [-1]), bins='auto')\n",
        "pbar.bar.close()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nqEyEhWie_7C"
      },
      "source": [
        "### `sample_sequential_monte_carlo` supports reproducible sampling"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Y3LkftGfh3tO"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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ATwJvr6ofjLueUauq54Ed3bXDe5K8vKrmvA6zrkK+qv5woe1J/gL4E+CaauDe0n7nu070fcSG1rYkFzMb8HdV1afGXc9KqqrvJXmQ2eswc4a80zWdJNcCfw38aVX9cNz1aGh8xEbDkgS4AzheVR8Ydz0rIcnE+bv/krwQeC3wtfn6G/I/9Q/Ai4HDSY4k+fC4CxqlJK9Pcgp4FXBfks+Ou6ZR6C6mn3/ExnHgYMuP2EjyceA/gN9KcirJLeOuacReDdwMXN39d3skyXXjLmrENgEPJjnK7CDmcFV9er7OfuNVkhrmSF6SGmbIS1LDDHlJapghL0kNM+QlqWGGvCQ1zJCXpIYZ8pLUsP8D2qbtUARUlg4AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tf.Tensor(\n",
            "[ 0.665834    0.9892149   0.7961128   1.0016634  -1.000767   -0.19461267\n",
            "  1.3070581   1.127177    0.9940303   0.58239716], shape=(10,), dtype=float32)\n",
            "different: tf.Tensor(\n",
            "[ 1.3284367   0.4374407   1.1349089   0.4557473   0.06510283 -0.08954388\n",
            "  1.1735026   0.8170528   0.12443061  0.34413314], shape=(10,), dtype=float32)\n",
            "same: tf.Tensor(\n",
            "[ 0.665834    0.9892149   0.7961128   1.0016634  -1.000767   -0.19461267\n",
            "  1.3070581   1.127177    0.9940303   0.58239716], shape=(10,), dtype=float32)\n"
          ]
        }
      ],
      "source": [
        "initial_state = tf.random.uniform([4096], -2., 2.)\n",
        "def smc(seed):\n",
        "  return tfp.experimental.mcmc.sample_sequential_monte_carlo(\n",
        "    prior_log_prob_fn=lambda x: -x**2 / 2,\n",
        "    likelihood_log_prob_fn=lambda x: -(x-1.)**2 / 2,\n",
        "    current_state=initial_state,\n",
        "    seed=seed)[1]\n",
        "plt.hist(smc(seed=(12, 34)), bins='auto');plt.show()\n",
        "\n",
        "print(smc(seed=(12, 34))[:10])\n",
        "print('different:', smc(seed=(10, 20))[:10])\n",
        "print('same:', smc(seed=(12, 34))[:10])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VHRVSmUJkx7q"
      },
      "source": [
        "### Added streaming computations of variance, covariance, Rhat\n",
        "Note, the interfaces to these have changed somewhat in `tfp-nightly`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7ZbXaMHnqHKl"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1008x576 with 20 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def cov_to_ellipse(t, cov, mean):\n",
        "  \"\"\"Draw a one standard deviation ellipse from the mean, according to cov.\"\"\"\n",
        "  diag = tf.linalg.diag_part(cov)\n",
        "  a = 0.5 * tf.reduce_sum(diag)\n",
        "  b = tf.sqrt(0.25 * (diag[0] - diag[1])**2 + cov[0, 1]**2)\n",
        "  major = a + b\n",
        "  minor = a - b\n",
        "  theta = tf.math.atan2(major - cov[0, 0], cov[0, 1])\n",
        "  x = (tf.sqrt(major) * tf.cos(theta) * tf.cos(t) -\n",
        "       tf.sqrt(minor) * tf.sin(theta) * tf.sin(t))\n",
        "  y = (tf.sqrt(major) * tf.sin(theta) * tf.cos(t) +\n",
        "       tf.sqrt(minor) * tf.cos(theta) * tf.sin(t))\n",
        "  return x + mean[0], y + mean[1]\n",
        "\n",
        "fig, axes = plt.subplots(nrows=4, ncols=5, figsize=(14, 8), \n",
        "                         sharex=True, sharey=True, constrained_layout=True)\n",
        "t = tf.linspace(0., 2 * np.pi, 200)\n",
        "tot = 10\n",
        "cov = 0.1 * tf.eye(2) + 0.9 * tf.ones([2, 2])\n",
        "mvn = tfd.MultivariateNormalTriL(loc=[1., 2.],\n",
        "                                 scale_tril=tf.linalg.cholesky(cov))\n",
        "\n",
        "for ax in axes.ravel():\n",
        "  rv = tfp.experimental.stats.RunningCovariance(\n",
        "      num_samples=0., mean=tf.zeros(2), sum_squared_residuals=tf.zeros((2, 2)),\n",
        "      event_ndims=1)\n",
        "\n",
        "  for idx, x in enumerate(mvn.sample(tot)):\n",
        "    rv = rv.update(x)\n",
        "    ax.plot(*cov_to_ellipse(t, rv.covariance(), rv.mean),\n",
        "            color='k', alpha=(idx + 1) / tot)\n",
        "  ax.plot(*cov_to_ellipse(t, mvn.covariance(), mvn.mean()), 'r')\n",
        "fig.suptitle(\"Twenty tries to approximate the red covariance with 10 draws\");"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UwebvDOFIpQ4"
      },
      "source": [
        "## Math, stats"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UVrlCesAIqZN"
      },
      "source": [
        "### Bessel functions: ive, kve, log-ive"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AQkxEJfW4ghp"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "xs = tf.linspace(0.5, 20., 100)\n",
        "ys = tfp.math.bessel_ive([[0.5], [1.], [np.pi], [4.]], xs)\n",
        "zs = tfp.math.bessel_kve([[0.5], [1.], [2.], [np.pi]], xs)\n",
        "\n",
        "for i in range(4):\n",
        "  plt.plot(xs, ys[i])\n",
        "plt.show()\n",
        "\n",
        "for i in range(4):\n",
        "  plt.plot(xs, zs[i])\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MP3kOPlMh7Rz"
      },
      "source": [
        "### Optional `weights` arg to `tfp.stats.histogram`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cp0GQ4yCZjRJ"
      },
      "outputs": [
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "edges = tf.linspace(-4., 4, 31)\n",
        "samps = tfd.TruncatedNormal(0, 1, -4, 4).sample(100_000, seed=(123, 456))\n",
        "_, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 3))\n",
        "ax1.bar(edges[:-1], tfp.stats.histogram(samps, edges))\n",
        "ax1.set_title('samples histogram')\n",
        "ax2.bar(edges[:-1], tfp.stats.histogram(samps, edges, weights=1 / tfd.Normal(0, 1).prob(samps)))\n",
        "ax2.set_title('samples, weighted by inverse p(sample)');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZQSVnu5re3S5"
      },
      "source": [
        "### `tfp.math.erfcinv`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fsb9Q4UT5HU6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tf.Tensor(\n",
            "[-3.         -2.3333333  -1.6666666  -1.         -0.33333325  0.3333335\n",
            "  1.          1.666667    2.3333335   3.        ], shape=(10,), dtype=float32)\n",
            "tf.Tensor(\n",
            "[-3.0002644  -2.3333426  -1.6666666  -0.9999997  -0.3333332   0.33333346\n",
            "  0.9999999   1.6666667   2.3333335   3.0000002 ], shape=(10,), dtype=float32)\n"
          ]
        }
      ],
      "source": [
        "x = tf.linspace(-3., 3., 10)\n",
        "y = tf.math.erfc(x)\n",
        "z = tfp.math.erfcinv(y)\n",
        "print(x)\n",
        "print(z)"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "TFP_Release_Notebook_0_12_1.ipynb",
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
